Step |
Hyp |
Ref |
Expression |
1 |
|
addcl |
|- ( ( A e. CC /\ B e. CC ) -> ( A + B ) e. CC ) |
2 |
|
subsub4 |
|- ( ( ( A + B ) e. CC /\ A e. CC /\ C e. CC ) -> ( ( ( A + B ) - A ) - C ) = ( ( A + B ) - ( A + C ) ) ) |
3 |
1 2
|
stoic4a |
|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( ( A + B ) - A ) - C ) = ( ( A + B ) - ( A + C ) ) ) |
4 |
|
pncan2 |
|- ( ( A e. CC /\ B e. CC ) -> ( ( A + B ) - A ) = B ) |
5 |
4
|
3adant3 |
|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A + B ) - A ) = B ) |
6 |
5
|
oveq1d |
|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( ( A + B ) - A ) - C ) = ( B - C ) ) |
7 |
3 6
|
eqtr3d |
|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A + B ) - ( A + C ) ) = ( B - C ) ) |